Ok, here is my two cents.  I used to work as an apartment manager.  We had a no pets policy.  At one point we decided to allow small pets.  Cats and Dogs under a certain weight.  Well....that did not go over well.  Tenants completely took advantage.  They we went back to the no pets policy, but allowed the cats and small dogs from when we had the pet policy in affect.  The large dogs had to leave.  This caused a fuss for the new people moving in.  "They have a pet, we can't we!!!"  And would try to sneak them in, and then we would have to send notices.   
I would take to you LL about it.  If he says no, then, do not sneak a pet of any kind in.  It will only cause problems.  For you, and for them.  And, you will most likely either have to find a new home, or re-home your little guy.  IF they allow it, make sure you don't "show off" your pet.     
Although....I hope they let you get a little guy.....        |